DFdistr {shotGroups}

Lookup table for distribution of range statistics and Rayleigh sigma

Description

Lookup table for the distribution of range statistics and Rayleigh sigma from a Monte Carlo simulation of circular bivariate normal shot groups with 0 mean and variance 1 in both directions. Includes the first four moments and several quantiles of the distribution of extreme spread, figure of merit, bounding box diagonal, and Rayleigh sigma for each combination of number of shots per group and number of groups, repeated 10 million times.

Usage

data(DFdistr)

Format

A data frame with 590 observations on the following 77 variables.

n

number of shots in each group. One of 2, 3, ..., 49, 50, 45, ..., 95, 100.

nGroups

number of groups with individual simulated range statistics that were averaged over to yield the final value. One of 1, 2, ..., 9, 10.

nShots

total number of shots, i.e., n*nGroups.

ES_M

Extreme spread mean over all Monte Carlo simulations

ES_V

Extreme spread variance over all Monte Carlo simulations

ES_SD

Extreme spread standard deviation over all Monte Carlo simulations

ES_CV

Extreme spread coefficient of variation over all Monte Carlo simulations

ESSQ_M

Squard extreme spread mean over all Monte Carlo simulations

ESSQ_V

Squared extreme spread variance over all Monte Carlo simulations

ES_SKEW

Extreme spread skewness over all Monte Carlo simulations (smoothed)

ES_KURT

Extreme spread kurtosis over all Monte Carlo simulations (smoothed)

ES_MED

Extreme spread median (50% quantile) over all Monte Carlo simulations

ES_Q005

Extreme spread 0.5% quantile over all Monte Carlo simulations

ES_Q025

Extreme spread 2.5% quantile over all Monte Carlo simulations

ES_Q050

Extreme spread 5% quantile over all Monte Carlo simulations

ES_Q100

Extreme spread 10% quantile over all Monte Carlo simulations

ES_Q250

Extreme spread 25% quantile over all Monte Carlo simulations

ES_Q500

Extreme spread 50% quantile (median) over all Monte Carlo simulations

ES_Q750

Extreme spread 75% quantile over all Monte Carlo simulations

ES_Q900

Extreme spread 90% quantile over all Monte Carlo simulations

ES_Q950

Extreme spread 95% quantile over all Monte Carlo simulations

ES_Q975

Extreme spread 97.5% quantile over all Monte Carlo simulations

ES_Q995

Extreme spread 99.5% quantile over all Monte Carlo simulations

FoM_M

Figure of merit mean over all Monte Carlo simulations

FoM_V

Figure of merit variance over all Monte Carlo simulations

FoM_SD

Figure of merit standard deviation over all Monte Carlo simulations

FoM_CV

Figure of merit coefficient of variation over all Monte Carlo simulations

FoM_SKEW

Figure of merit skewness over all Monte Carlo simulations (smoothed)

FoM_KURT

Figure of merit kurtosis over all Monte Carlo simulations (smoothed)

FoM_MED

Figure of merit median (50% quantile) over all Monte Carlo simulations

FoM_Q005

Figure of merit 0.5% quantile over all Monte Carlo simulations

FoM_Q025

Figure of merit 2.5% quantile over all Monte Carlo simulations

FoM_Q050

Figure of merit 0.25% quantile over all Monte Carlo simulations

FoM_Q100

Figure of merit 10% quantile over all Monte Carlo simulations

FoM_Q250

Figure of merit 25% quantile over all Monte Carlo simulations

FoM_Q500

Figure of merit 50% quantile (median) over all Monte Carlo simulations

FoM_Q750

Figure of merit 75% quantile over all Monte Carlo simulations

FoM_Q900

Figure of merit 90% quantile over all Monte Carlo simulations

FoM_Q950

Figure of merit 95% quantile over all Monte Carlo simulations

FoM_Q975

Figure of merit 97.5% quantile over all Monte Carlo simulations

FoM_Q995

Figure of merit 99.5% quantile over all Monte Carlo simulations

D_M

Bounding box diagonal mean over all Monte Carlo simulations

D_V

Bounding box diagonal variance over all Monte Carlo simulations

D_SD

Bounding box diagonal standard deviation over all Monte Carlo simulations

D_CV

Bounding box diagonal coefficient of variation over all Monte Carlo simulations

D_SKEW

Bounding box diagonal skewness over all Monte Carlo simulations (smoothed)

D_KURT

Bounding box diagonal kurtosis over all Monte Carlo simulations (smoothed)

D_MED

Bounding box diagonal median (50% quantile) over all Monte Carlo simulations

D_Q005

Bounding box diagonal 0.5% quantile over all Monte Carlo simulations

D_Q025

Bounding box diagonal 2.5% quantile over all Monte Carlo simulations

D_Q050

Bounding box diagonal 5% quantile over all Monte Carlo simulations

D_Q100

Bounding box diagonal 10% quantile over all Monte Carlo simulations

D_Q250

Bounding box diagonal 25% quantile over all Monte Carlo simulations

D_Q500

Bounding box diagonal 50% quantile (median) over all Monte Carlo simulations

D_Q750

Bounding box diagonal 75% quantile over all Monte Carlo simulations

D_Q900

Bounding box diagonal 90% quantile over all Monte Carlo simulations

D_Q950

Bounding box diagonal 95% quantile over all Monte Carlo simulations

D_Q975

Bounding box diagonal 97.5% quantile over all Monte Carlo simulations

D_Q995

Bounding box diagonal 99.5% quantile over all Monte Carlo simulations

RS_M

Rayleigh sigma mean over all Monte Carlo simulations

RS_V

Rayleigh sigma variance over all Monte Carlo simulations

RS_SD

Rayleigh sigma standard deviation over all Monte Carlo simulations

RS_CV

Rayleigh sigma coefficient of variation over all Monte Carlo simulations

RS_SKEW

Rayleigh sigma skewness over all Monte Carlo simulations (smoothed)

RS_KURT

Rayleigh sigma kurtosis over all Monte Carlo simulations (smoothed)

RS_MED

Rayleigh sigma median (50% quantile) over all Monte Carlo simulations

RS_Q005

Rayleigh sigma 0.5% quantile over all Monte Carlo simulations

RS_Q025

Rayleigh sigma 2.5% quantile over all Monte Carlo simulations

RS_Q050

Rayleigh sigma 5% quantile over all Monte Carlo simulations

RS_Q100

Rayleigh sigma 10% quantile over all Monte Carlo simulations

RS_Q250

Rayleigh sigma 25% quantile over all Monte Carlo simulations

RS_Q500

Rayleigh sigma 50% quantile (median) over all Monte Carlo simulations

RS_Q750

Rayleigh sigma 75% quantile over all Monte Carlo simulations

RS_Q900

Rayleigh sigma 90% quantile over all Monte Carlo simulations

RS_Q950

Rayleigh sigma 95% quantile over all Monte Carlo simulations

RS_Q975

Rayleigh sigma 97.5% quantile over all Monte Carlo simulations

RS_Q995

Rayleigh sigma 99.5% quantile over all Monte Carlo simulations

Details

The Monte Carlo distribution used 10 million repetitions in each scenario. One scenario was a combination of the n shots in each group, and the nGroups groups over which individual range statistics were averaged. Values for n were 2, 3, ..., 49, 50, 45, ..., 95, 100. Values for nGroups were 1, 2, ... 9, 10.

Skewness and kurtosis were smoothed using separate linear spline fits for each number of groups except for kurtosis of Rayleigh sigma which was fitted using the density of the gamma distribution.

Used in range2sigma to estimate Rayleigh parameter sigma from range statistics, and in efficiency to estimate the number of groups and total shots required to estimate the confidence interval (CI) for Rayleigh sigma with a given coverage probability (CI level) and width.

See the following source for an independent simulation, and for the rationale behind using it to estimate Rayleigh sigma:

http://ballistipedia.com/index.php?title=Range_Statistics

An older eqivalent simulation with less repetitions was done by Taylor and Grubbs (1975).

References

Taylor, M. S., & Grubbs, F. E. (1975). Approximate Probability Distributions for the Extreme Spread (BRL-MR-2438). Aberdeen Proving Ground, MD: U.S. Ballistic Research Laboratory.

See Also

range2sigma, efficiency, getMaxPairDist, getBoundingBox, getRayParam

Examples

data(DFdistr)
str(DFdistr)